Question

2 log4 x= (x+2), then

Answer 1

\(\large\color{black}{ \displaystyle 2\log_4 x= x+2 }\) like this?

Answer 2

value x=?

Answer 3

the rules you need (respectively) are:

1. \(\Large\color{black}{ \displaystyle {\rm \color{red}{a}}\log_{\rm \color{blue}{b}} {\rm \color{green}{c}} ~\Rightarrow ~\log_{\rm \color{blue}{b}} ({\rm \color{green}{c}}^{\rm \color{red}{a}}) }\) (exponent in logarithms)


2. \(\Large\color{black}{ \displaystyle \log_{\rm \color{blue}{r}} {\rm \color{red}{s}}= {\rm \color{green}{t}}~~~~\Rightarrow ~~~~{\rm \color{blue}{r}}^{\rm \color{green}{t}}={\rm \color{red}{s}}}\)

Answer 4

first, apply the rule #1 to the left side.
What do you then get?

Answer 5

log4 x^2

Answer 6

yes, \(\large\color{slate}{ \log_4(x^2)= x+2 }\)

Answer 7

then apply the second rule

Answer 8

(you can treat \(\large\color{slate}{ x^2 }\) as a single variable when it comes to applying the second rule)

Answer 9

ok

Answer 10

oh, I see the problem you are running into

Answer 11

no simple solution